System and Method of Measuring Process Compliance

ABSTRACT

In one embodiment the present invention includes a computer-implemented method of measuring process compliance. The method includes storing an adopted reference model of a business process and storing process instances of the business process. The method further includes generating an as-is model from the plurality of process instances. The method further includes calculating a sequence-based compliance measurement between the adopted reference model and the as-is model. The method further includes outputting the sequence-based compliance measurement. The sequence-based compliance measurement may be used to evaluate or to improve the business process.

CROSS REFERENCE TO RELATED APPLICATIONS

Not applicable.

BACKGROUND

The present invention relates to process compliance, and in particular,to process compliance measurement.

Unless otherwise indicated herein, the approaches described in thissection are not prior art to the claims in this application and are notadmitted to be prior art by inclusion in this section.

Reference models offer a set of generally accepted processes that aresound and efficient. Their adoption is generally motivated by thefollowing reasons. First, they significantly speed up the design ofprocess models by providing reusable and high quality content. Second,they optimize the design as they have been developed over a long periodand usually capture the business insight of experts. See W. M. P. vander Aalst, A. Dreiling, F. Gottschalk, M. Rosemann, and M.Jansen-Vullers, Configurable Process Models as a Basis for ReferenceModeling, in C. Bussler et al. (eds.), BPM '05: Intl. Workshops on theBusiness Process Reference Models, vol. 3812 of LNCS, pages 512-518(Springer Berlin, 2006). Third, they ease the compliance with industryregulations and requirements and, thus, mitigate risk. Fourth, they arean essential means to create a link between the business needs andinformation technology (IT) implementations. See W. M. P. van der Aalstet al. (previously cited above).

The Information Technology Infrastructure Library (ITIL) is a set ofguidance published as a series of books by the Office of GovernmentCommerce. These books describe an integrated best practice approach tomanaging and controlling IT services. See OGC, Official Introduction tothe ITIL Service Lifecycle (Stationery Office Books, London, 2007). TheControl Objectives for Information and related Technology (COBIT) hasbeen developed by the IT Governance Institute to describe goodpractices, to provide a process framework and to present activities in amanageable and logical structure. The Supply Chain Operations ReferenceModel (SCOR) provides a unique framework, which links business processand technology features into a unified structure to supportcommunication among supply chain partners and to improve theeffectiveness of supply chains. See Supply-Chain Council, Supply ChainOperations Reference Model (SCOR, 2006).

A process is compliant in terms of the introduced reference models ifthe process is implemented as described by the reference model and theprocess and its results comply with laws, regulations and contractualarrangements. See W. M. P. van der Aalst. Verification of Workflow Nets,in ICATPN '97: Intl. Conf. on Application and Theory of Petri Nets,pages 407-426 (Springer Berlin, London, UK, 1997). Other popularreference models include the APQC Process Classification Framework SM(PCF) (see APQC, American Productivity & Quality Center,<www.apqc.org/pcf>, 2008) and the Capability Maturity Model Integration(CMMI) (see CMMI, Software Engineering Institute,<www.sei.cmu.edu/cmmi/>, 2007).

Process mining algorithms have shown a considerable potential forassessing the compliance of instances with reference models. See A. K.Alves de Medeiros, A. J. M. M. Weijters, and W. M. P. van der Aalst,Genetic Process Mining: A Basic Approach and its Challenges, in C.Bussler and A. Haller (eds.), BPM '05: Intl. Workshops on BusinessProcess Management, vol. 3812 of LNCS, pages 203-215 (Springer Berlin,Nancy, France, 2006); A. Rozinat, M. Veloso, and W. M. P. van der Aalst,Evaluating the Quality of Discovered Process Models, in W. Bridewell etal. (eds.), IPM '08: Intl. Workshop on the Induction of Process Models,pages 45-52 (Antwerp, Belgium, 2008). The instances are typicallyrecorded by process-aware IS and serve as a starting point forreconstructing an as-is process model. The derived model can be comparedwith other models (e.g. reference models) using existing algorithms todetermine the equivalence of processes.

SUMMARY

Embodiments of the present invention improve process compliancemeasurement. In one embodiment the present invention includes acomputer-implemented method of measuring process compliance. The methodincludes storing an adopted reference model of a business process andstoring process instances of the business process. The method furtherincludes generating an as-is model from the plurality of processinstances. The method further includes calculating a sequence-basedcompliance measurement between the adopted reference model and the as-ismodel. The method further includes outputting the sequence-basedcompliance measurement. The sequence-based compliance measurement may beused to evaluate or to improve the business process.

According to an embodiment, compliance may be measured between anadopted reference model and a to-be model. According to an embodiment,compliance may be measured between a to-be model and as-is model.

According to an embodiment, the sequence-based compliance measurementmay be used to identify a process instance that negatively impacts theperformance of the business process.

According to an embodiment, a model may be adjusted according to one ormore of a granularity, an order partition, an exclusion partition, and acycle.

According to an embodiment, the sequence-based compliance measurementmay be used to iteratively adjust the to-be process model, to seewhether the adjustment results in an improvement of the businessprocess.

According to an embodiment, the sequence-based compliance measurementmay include one or more of a compliance degree, a compliance maturity, afiring sequence compliance, a firing sequence compliance degree, and afiring sequence compliance maturity.

According to an embodiment, a computer-readable medium embodying acomputer program may control a computer system to measure processcompliance, in a manner similar to that described above. According to anembodiment, a computer system may measure process compliance, in amanner similar to that described above.

The following detailed description and accompanying drawings provide abetter understanding of the nature and advantages of the presentinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing various business process models andcompliance relationships, according to an embodiment of the presentinvention.

FIG. 2 is a block diagram showing two event-driven process chains,according to an embodiment of the present invention.

FIG. 3 is a block diagram showing partitions, according to an embodimentof the present invention.

FIG. 4 is a block diagram of a computer system that implements acompliance measurement processes, according to an embodiment of thepresent invention.

FIG. 5 is a flow diagram of a method of measuring process compliance,according to an embodiment of the present invention.

FIG. 6 is a flow diagram of a method of adjusting a to-be process modelto improve the sequence-based compliance measurement, according to anembodiment of the present invention.

FIG. 7 is a block diagram of an example computer system and network forimplementing an embodiments of the present invention.

FIG. 8 is a screen shot showing an example workflow net.

FIG. 9 is a screen shot showing an example mapping.

DETAILED DESCRIPTION

Described herein are techniques for measuring compliance of a businessprocess. In the following description, for purposes of explanation,numerous examples and specific details are set forth in order to providea thorough understanding of the present invention. It will be evident,however, to one skilled in the art that the present invention as definedby the claims may include some or all of the features in these examplesalone or in combination with other features described below, and mayfurther include modifications and equivalents of the features andconcepts described herein.

In the following description, various methods, processes and proceduresare detailed. Although particular steps may be described in a certainorder, such order is mainly for convenience and clarity. A particularstep may be repeated more than once, may occur before or after othersteps (even if those steps are otherwise described in another order),and may occur in parallel with other steps. A second step is required tofollow a first step only when the first step must be completed beforethe second step is begun. Such a situation will be specifically pointedout when not clear from the context.

In the following description, the term “we” is used. This term refers tothe actions of the inventors, as well as to the actions of an embodimentof the present invention (which may have been configured to operate in aparticular manner by the inventors). This usage choice results from adesire to avoid extensive use of the passive voice. In a similar manner,the term “our” also includes references to an embodiment of the presentinvention. For example, the wording “our process” is interchangeablewith the wording “an embodiment of the present invention”.

Reference models can be differentiated along their scope, theirgranularity, and the views, which are depicted in the model. SeeConfigurable Process Models as a Basis for Reference Modeling. Wedistinguish (1) reference models focusing on capturing domain-specificbest practices like ITIL, COBIT, and SCOR, and (2) configurablereference models, such as SAP Solution Manager, which aim at capturingthe functionalities of a software system. (For information on SAPSolution Manager, see SAP—Components & Tools of SAP NetWeaver: SAPSolution Manager.) Although the focus of this description is on thefirst class of models, we explain both classes shortly with respect totheir characteristics and their contribution to compliance.

The SAP Solution Manager of SAP NetWeaver provides configurablereference models for business scenarios. Their usage ensures quality ofthe IT solution and enables traceability of all changes and, thus,compliance to the organizational needs. Most of the enterprise resourceplanning (ERP) vendors have similar approaches to support theconfiguration and implementation procedure of an information systems(IS) landscape.

As discussed above, reference models provide a set of generally acceptedbest practices to create efficient processes to be deployed insideorganizations. However, a central challenge is to determine how thesebest practices are implemented in practice. One limitation of existingapproaches for measuring compliance is the assumption that thecompliance can be determined using the notion of process equivalence.Nonetheless, the use of equivalence algorithms is not adequate since twomodels can have different structures but one process can still becompliant with the other. An embodiment of the present invention isdirected to a process to measure the compliance of process models withreference models.

As discussed above, reference models have gained increasing attention,because they make a substantial contribution to design and executeprocesses efficiently. Obviously, reference models are useful, but towhich extent are these best practices adopted and implemented in aspecific business context?

As discussed above, process mining algorithms have shown a considerablepotential for assessing the compliance of instances with referencemodels. A study has evaluated the results of a compliance analysis usingprocess mining and equivalence algorithms, and has determined that theyare not sufficient in many situations. As an example, one studyevaluated the compliance of an as-is process model of a passengerairline with a reference model which had incorporated the fundamentalsof ITIL. See K. Gerke and G. Tamm, Continuous Quality Improvement of ITProcesses based on Reference Models and Process Mining, in AMCIS '09:Americas Conf. on Information Systems (San Francisco, Calif., August,2009). The study found that the techniques available yield low values ofcompliance which could not be confirmed by the passenger airline. Thisdifference was mainly due to: (1) different levels of details, (2)partial view of process mining, and (3) overemphasis of the order ofactivities. First, the level of detail characterizing a process differswidely when comparing a reference model with an as-is or to-be processmodel. Second, the derived as-is model only partially represents theprocesses of the airline. The execution of the processes does not onlyresult in log files but it also results in written record files, manualactivities as well as human knowledge. Information outside the reach ofprocess mining algorithms may compromise the results of compliance.Finally, reference models typically do not state whether dependenciesbetween activities are compulsory. As another example, in a study oncompliance using existing equivalence algorithms, the authors changedthe order of activities in a reference model. While the complianceshould remain the same since the reference model did not enforce aspecific order for the execution of the activities, the complianceyielded different results.

In the process of discovering the above-noted shortcomings of existingcompliance measurements, we developed an embodiment of the presentinvention as more fully detailed below. We also discuss the differencesbetween process equivalence and process compliance and argue for theneed of specific algorithms to measure the compliance between processes.We show that two models can have different structures but one processcan still be compliant with the other. Furthermore, we develop a newapproach and process to overcome the drawbacks identified. We measurethe compliance of an as-is process model of a German passenger airlinewith a reference model. To validate our methodology, we compare ourcompliance results with two existing approaches and explain why currentalgorithms are not suitable to evaluate the compliance.

Based on our experiences with business processes of the air travelindustry, we devised an approach and methodology to analyze thecompliance between processes. The methodology identifies five entities,illustrated in FIG. 1, which may be considered when measuring thecompliance with reference models: the meta reference model M₀, theadopted reference model M₁, the to-be process model M₂, the instances(of the to-be process model M₂), and the as-is process model M₃.Depending on the scope, a meta reference model M₀ may provide eithergenerally accepted processes or a set of abstract guidelines. In bothcases, and particularly in the latter case, the reference model M₁ needsto be adapted to the needs of an organization yielding a set ofprocesses M₂. The execution of the processes generates a set ofinstances. The analysis of these instances provides an as-is processmodel M₃ which reflects how a process M₂ was executed. The level ofcompliance can be measured by analyzing process models M₀, M₁, M₂, andM₃. Since M₀ is generally specified in natural language, we willconcentrate our study on analyzing models M₁, M₂, and M₃.

Model M₁ and M₂ may be mainly constructed manually, whereas M₃ may beusually inferred from log files. These log files serve as a startingpoint for process mining algorithms, which aim at the automaticextraction of process knowledge. Various algorithms have been developedand implemented in ProM to discover different types of process models.See A. K. Alves de Medeiros, A. J. M. M. Weijters, and W. M. P. van derAalst, Genetic Process Mining: A Basic Approach and its Challenges, inC. Bussler and A. Haller (eds.), BPM '05: Intl. Workshops on BusinessProcess Management, vol. 3812 of LNCS, pages 203-215 (Springer Berlin,Nancy, France, 2006); A. Rozinat, M. Veloso, and W. M. P. van der Aalst,Evaluating the Quality of Discovered Process Models, in W. Bridewell etal. (eds.), IPM '08: Intl. Workshop on the Induction of Process Models,pages 45-52 (Antwerp, Belgium, 2008). These algorithms include, forinstance, Petri nets or Event-driven Process Chains (EPCs). See W. M. P.van der Aalst, Verification of Workflow Nets, in ICATPN '97: Intl. Conf.on Application and Theory of Petri Nets, pages 407-426 (Springer Berlin,London, UK, 1997); B. F. van Dongen, R. Dikman, and J. Mendling,Measuring Similarity between Business Process Models, in CAISE '08(2008). ProM is a process mining workbench offering algorithms todiscover and verify process models.

Opposing the as-is process model and the to-be process model supportsthe identification of potential improvements and contributes to thedetermination of alternative actions.

We define process compliance as the degree to which a process modelbehaves in accordance to a reference model. The behavior is expressed bythe instances, which can be generated by the model.

FIG. 2 shows two EPCs capturing similar functionalities. Both are takenfrom the complaint handling process of a German passenger airline. Theprocess is supported by the application “Interaction Center” (IAC) ofthe SAP Customer Relationship Management (CRM) system. The IACfacilitates the processing of interactions between business partners.Each interaction is registered as an activity. Besides a complaintdescription, further information, such as associated documents (e.g.e-mails), may be related to activities. Based on the characteristics ofa complaint, an activity of the categories “Cust. Relations” or “Cust.Payment” is established. For example, complaints associated withpayments are processed by the “Cust. Payment” department.

The EPC in the center of the figure shows model M₁, which depicts threeactivities: Create incident, Categorize incident, and Prioritizeincident. The EPC on the right-hand side of the figure shows model M₂.Processing starts with an incoming complaint. Customers can complain bysending an e-mail or by filling an online form. In the latter case, thecustomer has to classify the complaint. In the former case, an employeehas to read the e-mail to understand the complaint and determine thecategory manually. To measure the compliance, we need to discusscharacteristics of business and reference models.

Compliance Maturity and Degree. Our case study has identified two majorconcerns when it comes to evaluating compliance with reference models.First, the passenger airline wanted to learn if its processes followedthe behavior recommended by the reference model. Second, the airlinewanted to inquire if all the behavior recommended by the reference modelwas being implemented. In the context of compliance, we refer to theformer as compliance degree and we denote the latter as compliancematurity. Let us consider the processing of incoming customercomplaints. Model M₁ may recommend accepting complaints either viae-mail, letter or phone. If the airline accepts complaints via the firsttwo mentioned communication channels only a part of the recommendationsis implemented. We say that the airline is partially mature with respectto compliance maturity. But the ones currently being implemented (e-mailand letter) correspond to what the reference model M₁ recommends. Insuch a case, we say that the airline is fully compliant with respect tocompliance degree.

Granularity of Models. Having two models M₁ and M₂ it may happen thatthe granularity characterizing the level of detail of activities varies.For example, in FIG. 2, the activity “Prioritize incident” exists inmodel M₁, but no such activity exists in model M₂. Furthermore, it ispossible that compliance applies to a set of activities, rather thanindividual activities. For example, the activity “Categorize incident”of model M₁ corresponds to a set of activities 210 in model M₂ in FIG.2. In order to account for the granularity we may identify thecorrespondence of activities. Correspondence is a mapping betweenactivities of model M₂ to activities of model M₁ where the functionalityof the activities is the same. Existing approaches, for example schemaor semantic matching, assume that the correspondence can be establishedautomatically based on the labels. See B. F. van Dongen, R. Dikman, andJ. Mendling, Measuring Similarity between Business Process Models, inCAISE '08 (2008); and M. Ehrig, A. Koschmider, and A. Oberweis,Measuring Similarity between Semantic Business Process Models, in APCCM'07: Asia-Pacific Conf. on Conceptual Modeling, pages 71-80(Darlinghurst, Australia, 2007). The examples of our use case show thatit is not realistic to only assume that equivalent activities may beidentified by considering similarities of labels. For example, theactivities “Create incident” in model M₁ and “Create customer'scomplaint” in model M₂ have the same functionality, but they havedifferent labels. Since the automatic mapping is not applicable, wefavor the manual mapping.

Customization of the Reference Model. It is often important to treatparts of model M₁ in a special way when measuring compliance. Forexample, since reference models do not typically state if the activitieshave to be executed exactly in a specified order, the order may notalways be important. We refer to these special parts as partitions. Apartition is a user-selected set of activities with a type, which can be“Order” or “Exclusion”. FIG. 3 shows that activities “Categorizeincident” and “Prioritize incident” in partition P₁ may be executed inan arbitrary order. A partition of type “Exclusion” allows thedefinition of activities that may be excluded from the complianceanalysis. Consider partition P₂. In our use case, the preprocessing ofan incident is not supported by the IS right now. However, a manualactivity corresponding to the functionality expressed by activity“Preprocess incident” is executed. To prevent the missing activity fromerroneously affecting the compliance, the activity is excluded.

Iteration. A special circumstance is the case in which an activity ispart of an arbitrary cycle in process M₂ while it is not in model M₁.This means that this activity can be executed repetitively, while inmodel M₁ it must be performed correctly in only one iteration. Forexample, in our use case, the activities “Search for a solution” and“Inform Customer” are performed repeatedly until the customer acceptsthe processing of the claim. The existence of the cycle increases thequality of the process and contributes to a higher degree of thecustomer satisfaction. Thus, even if ITIL does not explicitly recommenda cycle, the airline feels that this cycle in model M₂ does not affectthe compliance with model M₁—a contrast with a cycle, which purely meansto redo work. The latter cycle negatively affects the efficiency of aprocess. What makes it even more complicated is the fact that variousreference models neither contain cycles nor state a precise number ofrecommended iterations. Without knowing the semantics of cycles it isnot possible to state in general its effect on compliance.

Sequence-Based Compliance

Based on the requirements discussed above, we have developed acomputer-implemented process to measure the compliance of model M₂ or M₃with model M₁. One feature is that two models can have differentstructures but the algorithm can still judge one process to be compliantwith the other. FIG. 8, for example, illustrates that the process modelsare different, but we will show that they are compliant.

Previous sections have used the EPC language to model processes since itis easy to understand and it is widely used in the industry (e.g. thecommon language of our use case). An embodiment of the present inventionuses a more formal approach based on workflow nets (WF-nets) for thedesign of the compliance measurement process. WF-nets are described inW. M. P. van der Aalst, Verification of Workflow Nets, in ICATPN '97:Intl. Conf. on Application and Theory of Petri Nets, pages 407-426(Springer Berlin, London, UK, 1997). WF-nets are a formalism well suitedto analyze processes since there is a vast amount of research done inthis area. We define the degree of compliance based on the firingsequences of WF-nets.

Definition 1 (WorkFlow net). A WorkFlow net (WF-net) is a tuple M=(P, T,F, i, o) such that: P is a finite set of places, T is a finite set oftransitions, P∩T=Ø, F⊂(P×T)∪(T×P) is a set of arcs, iεP is the uniquesource place such that i=Ø, oεP is the unique sink place such thato=Ø, every node xεP∪T is on a path from i to o, where for each nodexεP∪T the set x={y|(y, x)εF} is the preset of x and x={y|(x, y)εF} isthe postset of x.

Transitions represent the activities of an instance. The input place (i)and the output place (o) of the WF-net express the entry point wheninstances are created and the exit point when instances are deleted. Thelast requirement ensures that there are no transitions and places whichdo not contribute to processing.

Definition 2 (Firing sequence). Let M=(P, T, F, i, o) be a WF-net andlet tεT be a transition of M. A marking K: P→

is a mapping defining the number of tokens per place. t is enabled in amarking K if (∀pεt) K(p)≧1. t fires from marking K to marking K′,denoted by K[t

K′, if t is enabled in K and (∀pεt) K′(p)=K(p)−1 and (∀pεt)K′(p)=K(p)+1. σ=

t₁, t₂, . . . , t_(n)

εT* is a firing sequence leading from a marking K₁ to a marking K_(n+1),denoted by K₁[σ

K_(n+1), if there are markings K₂, . . . , K_(n), such that K₁[t₁

K₂[t₂

. . . K_(n)[t_(n)

K_(n+1).

To capture relevant behavior we restrict ourselves to firing sequencesrepresenting process instances that are terminated properly.

Definition 3 (Complete sound firing sequences). Let M=(P, T, F, i, o) bea WF-net and σεT*. K_(i) is the initial marking with K_(i)(i)=1 and(∀p≠i) K_(i)(p)=0. K_(o) is the final marking with K_(o)(o)=1 and (∀p≠o)K_(o)(p)=0. σ is a complete sound firing sequence, if K_(i)[σ

K_(o). Let us use S(M) to denote the set of all complete sound firingsequences.

This definition ignores unsound behavior, for instance process instancesrunning into a deadlock or a livelock. When no ambiguity occurs, wesimply refer to σ as a firing sequence.

Since WF-nets can be considered as directed graphs, where P∪T is the setof nodes and F is the set of arcs, we use the standard graph-theoreticalnotion of a cycle.

Definition 4 (Cycle). A cycle in a WF-net M=(P, T, F, i, o) is asequence of nodes (x₁, . . . , x_(n))ε(P∪T)*, such that (∀1≦i<n) (x_(i),x_(i+1))εF and x₁=x_(n).

The existence of cycles causes the set S(M) to be in general infinite.Therefore, we restrict the number of unroll factors for cycles by avariable parameter. (We omit the parameter here and in subsequentequations since it has no significant effect to the equations and wewant to keep them readable.) We end up with a finite subset of S(M)denoted by S′(M). The set S′(M) grows exponentially in the number oftransitions |T|. (Note that despite the exponential growth, animplementation example [described below] using an embodiment of thepresent invention shows that our approach can be used in practice.) Ourstrategy to deal with cycles and their contribution to compliance amongcompeting requirements (see the requirements discussion above withreference to FIG. 2) is to equate cycles having no correspondence inmodel M₁ with the action of redoing work. The superfluous work may havea negative effect on the compliance values.

To account for the special characteristics of compliance with referencemodels, which we have identified above with reference to FIG. 2 andsurrounding text, we use several parameters in our process.

Definition 5 (Granularity mapping). Let M₁=(P₁, T₁, F₁, i₁, o₁) andM₂=(P₂, T₂, F₂, i₂, o₂) be two WF-nets where we refer to M₁ as thereference model and to M₂ as the process model. We use a mapping G:T₂→T₁ to map activity labels in the process model to activity labels inthe reference model. Since G can be non-injective, this mapping canhandle granularity differences between the two models. Let us use theterm “granularity mapping” for G.

Definition 6 (User-selected partition). Let M₁ be a reference model asstated in Def. 5. A user-selected partition of M₁ is a set oftransitions p⊂T₁ which can be of type exclusion or order. User-selectedpartitions of type exclusion are represented with p and those of typeorder with {hacek over (p)}. M₁ can have associated with it at most oneuser-selected partition of type exclusion and an arbitrary finite numberof user-selected partitions of type order. Let us use P to denote theset of all user-selected partitions associated with M₁.

Now that we have defined the parameters, we deduce the compliancemeasures.

Definition 7 (Extended firing sequence set, Mapped firing sequence set).Let M₁ and M₂ be the reference model and the process model as stated inDef. 5. Let P be the set of all user-selected partitions related to M₁and let G be the granularity mapping between M₁ and M₂. Let σ₁εT₁* andσ₂εT₂*. σ₁ ^(ext) (P) is the set of extended firing sequences of σ₁,which is derived from σ₁ by applying two actions to σ₁: (1) remove thetransitions in p from σ₁ and (2) generate the permutations of σ₁\ p forall user-selected partitions {hacek over (p)}. Let us use|σ₁|_(ext)=|σ₁′|(σ₁′εσ₁ ^(ext)(P)) to denote the length of an arbitraryextended firing sequence σ₁′ of σ₁. σ₂ ^(map)(G) is the set of mappedfiring sequences of σ₂, which is derived from σ₂ by applying G to alltransitions of σ₂, whereas for each subsequence of transitions of σ₂,which are mapped to the same transition t₁εT₁ only one occurrence of t₁is placed in the resulting sequences, but possibly at differentpositions resulting in several mapped sequences. Let us use|σ₂|_(map)=|σ₂′|(σ₂′εσ₂ ^(map)(P)) to denote the length of an arbitrarymapped firing sequence σ₂′ of σ₂.

Note that |σ₁|_(ext) is well defined. The length of all extendedsequences σ₁′εσ₁ ^(ext)(P) is equal since they differ only in the orderof transitions. The same holds for |σ₂|_(map). Removing transitions by pguarantees |σ₁|_(ext)≦|σ₁| and the mapping of possible multipletransitions to one transition ensures |σ₂|_(map)≦|σ₂|.

Definition 8 (Compliance measures). Let M₁, M₂, G and P be as stated inthe definitions above. Let σ₁ εT₁* and σ₂ εT₂*. The firing sequencecompliance (fsc) of σ₂ w.r.t. σ₁ is:

fsc(σ₂,σ₁ ,P,G)=max{lcs(s,s′)|sεσ ₁ ^(ext)(P),s′εσ ₁ ^(map)(G)  (1)

The firing sequence compliance degree (fscd) of σ₂ w.r.t. σ₁ is:

$\begin{matrix}{{{fscd}( {\sigma_{2},\sigma_{1},,} )} = \frac{{fsc}( {\sigma_{2},\sigma_{1},,} )}{{\sigma_{1}}_{map}}} & (2)\end{matrix}$

The firing sequence compliance maturity (fscm) of σ₂ w.r.t. σ₁ is:

$\begin{matrix}{{{fscm}( {\sigma_{2},\sigma_{1},,} )} = \frac{{fsc}( {\sigma_{2},\sigma_{1},,} )}{{\sigma_{1}}_{ext}}} & (3)\end{matrix}$

The compliance degree (cd) of M₂ w.r.t. M₁ is given by:

$\begin{matrix}{{{cd}( {M_{2},M_{1},,} )} = \frac{\sum\limits_{\sigma_{2} \in {S^{\prime}{(M_{2})}}}{\max\limits_{\sigma_{1} \in {S^{\prime}{(M_{1})}}}\{ {{fscd}( {\sigma_{2},\sigma_{1},,} )} \}}}{{S^{\prime}( M_{2} )}}} & (4)\end{matrix}$

The compliance maturity (cm) of M₂ w.r.t. M₁ is given by:

$\begin{matrix}{{{cm}( {M_{2},M_{1},,} )} = \frac{\sum\limits_{\sigma_{1} \in {S^{\prime}{(M_{1})}}}{\max\limits_{\sigma_{2} \in {S^{\prime}{(M_{2})}}}\{ {{fscm}( {\sigma_{2},\sigma_{1},,} )} \}}}{{S^{\prime}( M_{1} )}}} & (4)\end{matrix}$

Function lcs in (1) calculates the length of the longest commonsubsequence of two firing sequences. Having a firing sequence σ₁, wewould like to know if a firing sequence σ₂ is similar (or vice versa).Since the lcs function in (1) returns the longest common subsequence offiring sequences σ₁ and σ₂, the greater the value returned, the moresimilar the two firing sequences are. Since the firing sequences σ₁ andσ₂ can have various structures when they have an extended firingsequence set or/and a mapped firing sequence set, function fsc willselect the variation of σ_(i) and σ₂ which will yield a greatersimilarity of σ_(i) and σ₂ using function lcs. For more details on lcs,see L. Bergroth, H. Hakonen, and T. Raita, A Survey of Longest CommonSubsequence Algorithms, in SPIRE '00: 7th Intl. Symposium on StringProcessing Information Retrieval, page 39 (IEEE Computer Society,Washington, D.C., 2000).

The compliance degree (2) of a firing sequence σ₂ indicates the extentto which the transitions of σ₂ are executed according to thespecifications of a reference model expressed with σ₁ while preservingthe activity order. Having selected the variations (by extension ormapping) of σ₁ and σ₂ which yield the greater similarity between σ₁ andσ₂, we would like to analyze and quantify the similarity of σ₁ and σ₂.Moreover, we would like to evaluate how many of the transitions of σ₂are present in σ₁. Let us refer to this similarity with symbol ‘c’.Symbol ‘c’ indicates how many transitions are shared by the two firingsequences. If the value of ‘c’ is close to the length of firing sequenceσ₂, this implies that σ₁ is closely similar to σ₂. As a result, thisindicates that the transitions of firing sequence σ₂ are executed in asimilar way which is prescribed by σ₁ (a specification of a referencemodel). When such a case happens, function fscd (2) returns a valuewhich is close to 1. On the other hand, if σ₁ is strongly different whencompared to σ₂, this implies that their similarity value ‘c’ is low. Asa result, the number of transitions of σ₂ that follow the transitions ofσ₁ is also low, further resulting in a low compliance degree of σ₂ withthe specifications of a reference model expressed with σ₁.

The compliance maturity (3) of a firing sequence σ₂ points at the extentto which the specification of a reference model expressed with σ₁ isfollowed by σ₂. The explanation of the mechanics of this function issimilar to the explanation given from the previous function (function2). The main contrast is that in (3) we are interested in evaluating thetransitions of firing sequence σ₁ which are executed in a similar wayaccording to the sequence described by σ₂. If the value of ‘c’ is closeto the length of firing sequence σ₁, this implies that σ₂ is closelysimilar to σ₁. As a result, this indicates that the transitions offiring sequence σ₁ are executed in a similar way by σ₂. Therefore, thecompliance is high.

In (4), (5), the degree and maturity of compliance express the ratio ofinstances, which can be produced by one model that can also be producedby the other model. From the viewpoint of compliance degree, the processmodel is related to the reference model; from maturity, vice versa.Here, we rely on the use of functions fscd (2) and fscm (3), whichanalyze the compliance of individual firing sequences, to compute thebest match between all the firing sequences of M₁ and all the firingsequences of M₂. The overall computation adds the contribution of theindividual firing sequences that belong to a match between the twomodels. The contribution of individual firing sequences is then dividedby |S′(M₁)| or by |S′(M₂)|. |S′(M₁)| and |S′(M₂)| represent the totalnumber of instances present in M₁ and M₂, respectively. If we areinvestigating to analyze the compliance maturity, we divide by |S′(M₁)|since we want to investigate how many of the instances of M₁ are beingfollowed by instance of M₂. Otherwise, to compute the compliance degree,we divide by |S′(M₂)|. In this last case, we are investigating how manyinstance of M₂ are also present in M₁. The greater the number ofinstances, the greater the compliance degree.

These compliance measures return a value in interval [0; 1]. Forexample, if the compliance degree is 1, the compliance is the highestsince all firing sequences of model M₂ can also be produced by model M₁.

FIG. 4 is a block diagram of a computer system 400 that implements theabove processes, according to an embodiment of the present invention.The computer system 400 includes a number of client computers 402, aserver computer 404, and an analysis computer 406. A network 408connects the client computers 402, the server computer 404 and theanalysis client computer 406. The network 408 may be implemented withone or more network elements, e.g., local area network(s), wide areanetwork(s), the internet, etc.

The client computers 402 generate process instances (see, e.g., FIG. 1).For example, given a to-be process model that users of the clientcomputers 402 are following, they generate the process instances inaccordance with following the to-be process model M₂ (see also FIG. 1).The client computers 402 may generally implement the presentation tierof a three-tier architecture, e.g., to display information that ismanaged by the application tier or the database tier. The clientcomputers 402 communicate with the server computer 404.

The server computer 404 includes a storage system 420, a generationmodule 422, a calculation module 424, and an interface module 426. Thestorage system 420 stores an adopted reference model M₁ 430 (see alsoFIG. 1) and the process instance data 432 generated by the clientcomputers 402. (The adopted reference model M₁ 430 is related to theto-be process model M₂ as shown in FIG. 1.) The generation module 422generates an as-is model M₃ 434 from the process instance data 432. Thecalculation module calculates a sequence-based compliance measurementbetween the adopted reference model M₁ 430 and the as-is model M₃ 434.The interface module 426 outputs the sequence-based compliancemeasurement, for example to the analysis computer 406. The servercomputer 404 may generally implement the application tier in athree-tier architecture. (The database tier is not shown.)

The analysis computer 406 provides a user interface to interact with theserver 404 to measure compliance. A process analyst may use the analysiscomputer 406 to control the server computer 404 to execute thecompliance measurements discussed above.

According to an embodiment, the server computer 404 identifies a processinstance that negatively impacts the sequence-based compliancemeasurement. For example, if a user of a client computer 402 hasgenerated a process instance that is outside of compliance, then thiscan be identified (and corrective action can be taken to preventrecurrence of the non-compliance).

According to an embodiment, the server computer 404 adjusts the to-beprocess model according to the sequence-based compliance measurement,the client computers 402 generate additional process instances, and theserver computer 404 re-calculates the sequence-based compliancemeasurement. This process may be performed iteratively. In this manner,it can be determined whether adjusting the to-be process model resultsin an improvement of the business process. According to a furtherembodiment, adjustment of the to-be process model can involve humanintervention. This human intervention may include a manual approvalprocess of suggested modifications, or training for users to be madeaware of the modifications.

According to an embodiment, the analysis computer 406 implementsdirectly the functionality of the server computer 404 that is used toexecute the compliance measurements (and the server computer 404 doesnot). For example, when the server computer 404 and the client computers402 are operating in a production environment, the server computer 404implements the application tier for the business process; the operationof the analysis computer 406 then does not impact the productionenvironment.

FIG. 5 is a flow diagram of a method 500 of measuring processcompliance, according to an embodiment of the present invention. Themethod 500 may be implemented by the computer system 400 (see FIG. 4),for example, by executing one or more computer programs to control theoperation of the computer system 400 according to the processes of themethod 500. More specifically, parts of the method 500 may beimplemented by the server computer 404 (or by the analysis computer406).

In 502, an adopted reference model M₁ of a business process is stored.

In 504, a number of process instances of the business process arestored. The process instances may be recorded from the actions of usersfollowing a to-be process model M₂ of the business process.

In 506, an as-is model M₃ is generated from the process instances. Anoptional step 507 may be performed (see below).

In 508, a sequence-based compliance measurement is calculated betweenthe adopted reference model M₁ and the as-is model M₃.

In 510, the sequence-based compliance measurement is output. Thesequence-based compliance measurement may include two complianceindicators: compliance degree and compliance maturity.

In 512, a process instance that negatively impacts the sequence-basedcompliance measurement is identified. Corrective action may then betaken based on this identification to improve a future sequence-basedcompliance measurement.

According to an embodiment, in 507 the models may be prepared oradjusted. According to an embodiment, the adjustment 507 may occur priorto operation of a step such as the calculation step 508. The preparationof a model may include three substeps. First, the process model ismapped. The mapping may be accomplished in a manner similar to thatdiscussed above regarding FIG. 2 (note that the model may be adjustedaccording to the granularity, exclusion, etc.). Second, the referencemodel may be customized. The customization may be accomplished in amanner similar to that discussed above in the section “Customization ofthe Reference Model”. Third, any iterations may be accommodated in themodel, in a manner similar to that discussed above in the section“Iteration”.

FIG. 6 is a flow diagram of a method 600 of adjusting a to-be processmodel M₂ to improve the sequence-based compliance measurement, accordingto an embodiment of the present invention. The process instances aregenerated according to the to-be process model M₂, which is developedfrom the adopted reference model M₁ (see FIG. 1). The method 600 may beperformed iteratively, or continuously, in order to improve thesequence-based compliance measurements made according to the method 500.The method 600 may be performed by the computer system 400 (see FIG. 4)in a manner similar to that discussed above with reference to FIG. 5.The method 600 may involve human intervention similar to that discussedabove.

In 602, the to-be process model M₂ is adjusted according to the sequencebased compliance measurement to produce an adjusted to-be process model.For example, the sequence based compliance measurement (see FIG. 5) mayindicate that the business process is less than fully compliant with theadopted reference model M₁, which indicates improvement may be possible.

In 604, a second set of process instances are recorded according to theadjusted to-be process model. More specifically, the users are now usingthe adjusted to-be process model instead of the original to-be processmodel.

In 604, an adjusted as-is model is generated from the second set ofprocess instances (see 506 in FIG. 5).

In 606, an adjusted sequence-based compliance measurement between theadopted reference model and the adjusted as-is model is generated (see508 in FIG. 5).

In 608, the adjusted sequence based compliance measurement is comparedwith the sequence based compliance measurement, to determine whether theadjusted to-be process model resulted in an improvement of the businessprocess.

As described above, an embodiment of the present invention measurescompliance between the adopted reference model M₁ and the as-is modelM₃. Note that other embodiments may measure the compliance between othermodels (see, e.g., FIG. 1). According to an embodiment, compliance ismeasured between the adopted reference model M₁ and the to-be processmodel M₂. According to an embodiment, compliance is measured between theto-be process model M₂ and the as-is model M₃.

FIG. 7 is a block diagram of an example computer system and network 700for implementing embodiments of the present invention. Computer system710 includes a bus 705 or other communication mechanism forcommunicating information, and a processor 701 coupled with bus 705 forprocessing information. Computer system 710 also includes a memory 702coupled to bus 705 for storing information and instructions to beexecuted by processor 701, including information and instructions forperforming the techniques described above. This memory may also be usedfor storing temporary variables or other intermediate information duringexecution of instructions to be executed by processor 701. Possibleimplementations of this memory may be, but are not limited to, randomaccess memory (RAM), read only memory (ROM), or both. A storage device703 is also provided for storing information and instructions. Commonforms of storage devices include, for example, a hard drive, a magneticdisk, an optical disk, a CD-ROM, a DVD, a flash memory, a USB memorycard, or any other medium from which a computer can read. Storage device703 may include source code, binary code, or software files forperforming the techniques or embodying the constructs above, forexample.

Computer system 710 may be coupled via bus 705 to an output device 712,such as a cathode ray tube (CRT) or liquid crystal display (LCD), fordisplaying information to a computer user. An input device 711 such as akeyboard and/or mouse is coupled to bus 705 for communicatinginformation and command selections from the user to processor 701. Thecombination of these components allows the user to communicate with thesystem. In some systems, bus 705 may be divided into multiplespecialized buses.

Computer system 710 also includes a network interface 704 coupled withbus 705. Network interface 704 may provide two-way data communicationbetween computer system 710 and the local network 720. The networkinterface 704 may be a digital subscriber line (DSL) or a modem toprovide data communication connection over a telephone line, forexample. Another example of the network interface is a local areanetwork (LAN) card to provide a data communication connection to acompatible LAN. Wireless links is also another example. In any suchimplementation, network interface 704 sends and receives electrical,electromagnetic, or optical signals that carry digital data streamsrepresenting various types of information.

Computer system 710 can send and receive information, including messagesor other interface actions, through the network interface 704 to anIntranet or the Internet 730. In the Internet example, softwarecomponents or services may reside on multiple different computer systems710 or servers 731, 732, 733, 734 and 735 across the network. A server731 may transmit actions or messages from one component, throughInternet 730, local network 720, and network interface 704 to acomponent on computer system 710.

According to an embodiment, the client computer 402 (see FIG. 4) may beimplemented by the computer system 710. According to an embodiment, theanalysis computer 406 (see FIG. 4) may be implemented by the computersystem 710. According to an embodiment, the server computer 404 (seeFIG. 4) may be implemented by the server 731, which may include internalcomponents similar to those of the computer system 710.

Operational Example

This section applies the sequence-based compliance analysis to the casestudy discussed above and compares the results with two existingapproaches available in ProM: “Structural Precision/Recall” and“Footprint Similarity”. We have chosen these two approaches since theyare sometimes used to determine the compliance between models. Wediscuss the results of our study below.

Measuring Sequence-based Compliance. FIG. 8 shows the starting point forthe compliance analysis in ProM: two WF-nets. The left-hand side modelportrays the reference model M₁, which was adopted from ITIL. Initiallycreated as an EPC in the ARIS toolset, it has been converted into aWF-net and imported into ProM. The right-hand side model illustrates theas-is model M₃, which represents the complaint handling process of thepassenger airline. It was extracted with the ProM plugin “HeuristicMiner” from a log file containing 4,650 cases and 44,006 events beingobserved over a period of one year. (Further details of the HeuristicMiner can be found at <www.processmining.org>.)

To adapt the reference model to the needs of the airline, model M₁ wascustomized as follows. The activity Identify responsible employee wasexcluded because the activity was not recorded by the IS. The airlineassumes that the activities Inform customer and Preprocess incident maybe executed in an arbitrary order. As a result, the airline has agreedon a user-selected partition of type exclusion ( p={Identify responsibleemployee}) as well as on a partition of type order ({hacek over(p)}={Inform customer, Preprocess incident}). Besides the user-selectedpartitions, the left-hand side of FIG. 9 shows the granularity mapping.Please note, that the figure denotes the adopted reference model M₁ andthe as-is model M₂. During the mapping, we found typical characteristicsin the airline process discussed above (see FIG. 2 and related text):missing and additional activities and activities with different levelsof detail. For example, the activity “Prioritize incident” is missing inmodel M₃ and the activities “Create activity Cust. Relations” and“Create activity Cust. Payments” of model M₃ correspond to the activity“Create incident” in model M₁. FIG. 8 shows that the airline usesiterations: model M₃ has cycles. Since the cycles are seen as qualityimprovement, the limit for cycle detection is set to 1. This limitensures that all activities are considered but that the iteration ofactivities is not punished.

The right-hand side of FIG. 9 illustrates the results of our complianceanalysis. Visible are the compliance degree and compliance maturity,which were computed according to Equations (4 and 5) per passed cycle aswell as the extended firing sequences σ₁ ^(ext)(P) of model M₁ and thefiring sequences σ₃ ^(map)(G) of model M₃. Unrolling a cycle once,yields the compliance degree cd(M₃, M₁, P, G) of 0.82 and the compliancematurity cm(M₃, M₁, P, G) of 0.52. To explain these values, we study thefirst line of the sequences σ_(i) and σ₃, respectively. We consider thefollowing extended firing sequence σ′₁₋₁=

Receive incident, Identify account, Create incident record, Processincident, Categorize incident, Prioritize incident, Search for asolution, Make solution available, Inform customer, Preprocess incident,Close incident

and σ″₁₋₁=

Receive incident, Identify account, Create incident record, Processincident, Categorize incident, Prioritize incident, Search for asolution, Make solution available, Preprocess incident, Inform customer,Close incident

, σ′₁₋₁, σ″₁₋₁εσ₁ ^(ext)(P). Let us also consider the firing sequenceσ₃₋₁=

Open complaint, Receive contact, Edit mail, Classify problem, Identifyaccount, Create activity Cust. Relations, System allocates flight data,Close complaint

, which results in the firing sequence σ′₃₋₁=

Receive incident, Categorize incident, Identify account, Create incidentrecord, Process incident, Close incident

εσ₃ ^(map)(G). Since the maximum common longest subsequence of σ′₁₋₁ andσ″₁₋₁ with σ′₃₋₁ corresponds to

Receive incident, Identify account, Create incident record, Processincident, Close incident

, the firing sequence compliance fsc(σ₃₋₁, σ₁₋₁, P, G) is 5. The firingsequence compliance degree fscd(σ₃₋₁, σ₁₋₁, P, G) is ⅚. This means thatthe instance σ₃₋₁ of the as-is process model follows the order of thereference model with an overlap of 83%. The firing sequence compliancematurity fscm(σ₃₋₁, σ₁₋₁, P, G) is 5/11. This means that only 45% ofinstance σ₁₋₁ prescribed by the reference model are being followed byinstance σ₃₋₁ of the as-is process model. The result of the compliancedegree of 82% indicates that the processes executed by the airlinecorrespond to the recommendations of the reference model. We can saythat, although the models M₃ and M₁ look different, the model M₃ ishighly compliant with reference model M₁. The compliance maturity of 52%indicates that there are recommendations in reference model M₁ which arenot implemented by the airline. Nonetheless, because of the maturityvalue of 52% we can conclude that model M₃ is also partially mature withreference model M₁.

Measuring Precision and Recall. Structural precision and recall areintroduced in W. M. P. van der Aalst, A. K. Alves de Medeiros, and A. J.M. M. Weijters, Process Equivalence: Comparing Two Process Models Basedon Observed Behavior, in BPM '06: Intl. Conf. on Business ProcessManagement, vol. 4102, pages 129-144 (Springer Berlin, 2006).Precision^(S) (M₁, M₂) is the fraction of connections in M₂ that alsoappear in M₁. If this value is 1, the precision is the highest becauseall connections in the second model exist in the first model. Recall^(S)(M₁, M₂) is the fraction of connections in M₁ that also appear in M₂. Ifthe value is 1, the recall is the highest because all connections in thefirst model exist in the second model. To analyze the compliance, modelM₁ and M₃ of our use case need to be represented by a heuristic net.Therefore, we have converted model M₁, originally represented by an EPC,into a Heuristic net using ProM. Since the ProM plugin expects samelabels, we have renamed the labels of model M₃ according to model M₁ andcarried out the mapping depicted in FIG. 9. The structural precisionobtained was 3% and the recall was 8%.

Measuring Causal Footprint. The causal footprint is the second approachwe have compared with our process. (The causal footprint is described inB. F. van Dongen, R. Dikman, and J. Mendling, Measuring Similaritybetween Business Process Models, in CAISE '08 [2008].) The footprintidentifies two relationships between activities: look-back andlook-ahead links. The present detailed description does not elaborate onthe corresponding equation due to its complexity. Since the analysis ofthe causal footprint is based on comparing two EPCs, we have convertedmodel M₃ into an EPC using a conversion plugin in ProM. According to anembodiment, the mapping was manually performed in accordance to themapping shown in FIG. 9. To analyze the causal footprint, the ProMplugin “Footprint Similarity” was used and yielded a result of 27%.

Evaluation

This section discusses the compliance values, which we yielded in theOperational Example section above based on the requirements discussedabove with reference to FIG. 2 and related text.

Precision and recall rely on the notion of equivalence and expectprocess models, which need to be compared, to be equal in theirstructure. This is the reason why the values obtained are relativelylow: 3% and 8%, respectively. Similar to our approach, these twomeasures allow an analysis of the compliance from the perspectivescompliance degree (i.e. precision) and compliance maturity (i.e.recall). By contrast, the approach neither offers a mappingfunctionality nor accounts for the necessary customization of thereference model: ordering or exclusion of activities. Expressing thebehavior of a model in terms of connections results in the loss ofinformation whether two connected transitions are part of a cycle andneglects the control flow of process models. However, these are relevantinformation when measuring the compliance with reference models.

The causal footprint also relies on the notion of equivalence. However,the approach assumes that process models with different structures maybe similar. Therefore, the result of 27% is closer to the valuesobtained when using the process we have developed (i.e. 82% and 52%).Since the formula is symmetric, measuring the compliance of model M₃with model M₁ or of model M₁ with model M₃ yields the same value. It isclear that this situation is perfectly aligned with the notion ofequivalence but fails to meet the requirements of determining compliancefrom the perspectives degree and maturity. Like our approach, the notionof mapping is included in the plugin. However, a non-injective mappingis not supported. Since the algorithm accounts for the ordering ofactivities, it partially fulfills the requirements for customization ofreference models. Nonetheless, it does not account for the exclusion ofactivities. In B. F. van Dongen, R. Dikman, and J. Mendling, MeasuringSimilarity between Business Process Models, in CAISE '08 [2008], theauthors do not state the behavior of their formula with respect tocycles.

Using evaluation systems with the notion of equivalence, we are temptedto infer that the processes are not compliant. In contrast to thesequence-based compliance, the recall and precision and the causalfootprint yield a value, which is little expressive and hard to explain.It is not possible to trace the missing or dissent instances. Thesolution implemented according to an embodiment of the present inventionobtains two different values for compliance (i.e. degree and maturity)and also calculates intermediate results from instance compliance. Thisenables process designers to trace back which instances are affectingpositively or negatively the compliance of the processes under analysis.The industrial application shows that the notion of equivalence cannotbe used with satisfactory results to evaluate the compliance ofprocesses with a reference model.

Implementation Example

The sequence-based compliance algorithm is based on the generation ofsets of firing sequences to describe the behavior of a process model.Unfortunately, in general, the size of these sets can grow exponentiallywith the size of the WF-net in terms of activities. This section showsthe applicability of our process in spite of its exponential complexity.Similar to that described in R. Dijkman, Diagnosing Differences betweenBusiness Process Models, in BPM '08: Intl. Conf. on Business ProcessManagement, pages 261-277 (Springer Berlin, Heidelberg, 2008), we used asample of EPCs of the SAP reference model to test whether our processcan be applied in practice by showing that the computation times areacceptable. The SAP reference model has been described in other papers.See, e.g., A. Ladd T. Curran, G. Keller, SAP R/3 Business Blueprint:Understanding the Business Process Reference Model (Prentice Hall PTR,Enterprise Resource Planning Series, Upper Saddle River, 1997); and T.Teufel and G. Keller, SAP R/3 Process Oriented Implementation: IterativeProcess Prototyping (Addison-Wesley, 1998). Since it is among the mostcomprehensive reference models covering over 600 business processes, weassume that these models can be regarded as a representative example.The study is performed by applying the sequence-based compliance processto a subset of 126 pairs of EPCs from the SAP reference model, which wehave converted to WF-nets. The pairs are put together based on theirsimilarity computed by the ProM plugin “EPC Similarity Calculator”. Ourpairs are characterized with a similarity greater than 50%. Ninetypercent of the process models analyzed with an embodiment of the presentinvention took less than 62 milliseconds. In the implementation example,the runtime of the algorithm takes on average 50.5 milliseconds with astandard deviation of 9.3 milliseconds. (The hardware used for thisanalysis included an AMD™ dual core CPU running at 2.0 GHz, runningMicrosoft Windows Vista™ with 2 GB of memory.) The average number ofactivities in the processes of a model pair is 16. We only found a weakcorrelation between runtime and the number of activities of a process.Therefore, we conclude that for the number of activities, which we foundin the SAP reference models, the sequence-based compliance analysis isapplicable. These results show that, in theory we are confronted withexponential runtime when the complexity is measured in terms of theinput size only, i.e. activities. However, in practice there are naturalboundaries, e.g. the number of activities per process model is between alower bound and an upper bound. Hence, the process can be used inpractice despite its exponential complexity.

An alternative to address complexity with regard to the input size ofthe algorithm is to capture the behavior of a model using the statespace of a WF-net. A state space corresponds to the set of reachablemarkings of a WF-net. See T. Basten and W. M. P. van der Aalst,Inheritance of Behavior, in Journal of Logic and Algebraic Programming,47(2):47-145 (March/April 2001). The resulting graph is denoted as thereachability graph. In P. Buchholz and P. Kemper, HierarchicalReachability Graph Generation for Petri Nets, in Form. Methods Syst.Des., 21(3):281-315 (2002) is presented a method focusing on optimizingthe generation of the reachability graph of large Petri nets. Thecentral idea is to decompose a net, to generate reachability graphs forthe parts and to combine them. Furthermore, there exist varioustechniques for state space reduction (see R. Dijkman, DiagnosingDifferences between Business Process Models, in BPM '08: Intl. Conf. onBusiness Process Management, pages 261-277 [Springer Berlin, Heidelberg,2008]), which may be exploited to improve the efficiency of theunderlying algorithm of the sequence-based compliance algorithm.Corresponding approaches are referred to reduction rules. These rulesaim at reducing the size of the state space by reducing the number ofplaces and transitions preserving information relevant for analysispurpose. For example, it is possible to account for the significance oftransitions. Transitions, which are rarely executed, can be left outusing abstraction or encapsulation. Again, we found arguments for theapplicability of state spaces in the context of the input size. Forexample, Verbeek et al. argue that state spaces generating areachability graph are often feasible for systems up to 100 transitions.See H. M. W. Verbeek, Verification and Enactment of Workflow ManagementSystems, PhD thesis (University of Technology, Eindhoven, TheNetherlands, 2004).

CONCLUSION

As discussed above, reference models provide valuable recommendationsfor the implementation of business processes. However, methods andsolutions to determine how these guidelines are implemented in practiceare inexistent. Known algorithms to evaluate the equivalence ofprocesses have proven to be insufficient to measure compliance sincemany factors and characteristics related to compliance are ignored.

In developing an embodiment of the present invention, we haveinvestigated the characteristics of compliance and we have devised aprocess to analyze the compliance of process models with referencemodels. A feature of an embodiment of the present invention is aprocess, called sequence-based compliance, which is based on theobservation that process models can have different structures but oneprocess can still be compliant with the other.

In order to validate the practical operation of an embodiment of thepresent invention, we have measured the compliance of a complainthandling process of a German passenger airline. The passenger airlinehas obtained transparency of its current customer support processes bycarrying out process mining on their log files. Nonetheless, the nextstep, which was executed according to an embodiment of the presentinvention, was to determine to which extent the process were alignedwith a reference model (i.e. ITIL). This second step has beendemonstrated as discussed above.

We have further evaluated an embodiment of the present invention bycomparing the results with two existing approaches. The validation wasnot trivial since we applied process mining and equivalence algorithmson real data. The results have shown that the sequence-based complianceyields more insightful values when compared to the results of existingalgorithms based on analyzing the equivalence of processes.

The description has focused on an example implementation regarding thecomplaint handling process of a German passenger airline. Note that thiswas for illustrative purposes as well as for showing the feasibility ofthe implementation using actual data. Embodiments of the presentinvention may be used in other types of businesses and for other typesof business processes.

The above description illustrates various embodiments of the presentinvention along with examples of how aspects of the present inventionmay be implemented. The above examples and embodiments should not bedeemed to be the only embodiments, and are presented to illustrate theflexibility and advantages of the present invention as defined by thefollowing claims. Based on the above disclosure and the followingclaims, other arrangements, embodiments, implementations and equivalentswill be evident to those skilled in the art and may be employed withoutdeparting from the spirit and scope of the invention as defined by theclaims.

1. A computer-implemented method of measuring process compliance,comprising: storing, by a computer system, an adopted reference model ofa business process; storing, by the computer system, a plurality ofprocess instances of the business process; generating, by the computersystem, an as-is model from the plurality of process instances;calculating, by the computer system, a sequence-based compliancemeasurement between the adopted reference model and the as-is model; andoutputting, by the computer system, the sequence-based compliancemeasurement.
 2. The computer-implemented method of claim 1, furthercomprising: identifying, by the computer system, a process instance ofthe plurality of process instances that negatively impacts thesequence-based compliance measurement.
 3. The computer-implementedmethod of claim 1, wherein the plurality of process instances arerecorded according to a to-be process model, wherein the to-be processmodel is developed from the adopted reference model, further comprising:adjusting the to-be process model according to the sequence-basedcompliance measurement to produce an adjusted to-be process model;storing, by the computer system, a second plurality of process instancesthat were recorded according to the adjusted to-be process model;generating, by the computer system, an adjusted as-is model from thesecond plurality of process instances; calculating, by the computersystem, an adjusted sequence-based compliance measurement between theadopted reference model and the adjusted as-is model; and comparing theadjusted sequence-based compliance measurement with the sequence-basedcompliance measurement, to determine whether the adjusted to-be processmodel resulted in an improvement of the business process.
 4. Thecomputer-implemented method of claim 1, where calculating thesequence-based compliance measurement comprises: calculating acompliance degree between the adopted reference model and the as-ismodel; and calculating a compliance maturity between the adoptedreference model and the as-is model.
 5. The computer-implemented methodof claim 1, where calculating the sequence-based compliance measurementcomprises calculating a firing sequence compliance (fsc) of the as-ismodel with respect to the adopted reference model according to anequation:fsc(σ₂,σ₁ ,P,G)=max{lcs(s,s′)|sεσ ₁ ^(ext)(P),s′εσ ₁ ^(map)(G)} whereinthe firing sequence compliance selects a variation having a maximumsimilarity between a first firing sequence σ₁ and a second firingsequence σ₂.
 6. The computer-implemented method of claim 5, wherecalculating the sequence-based compliance measurement comprises:calculating a firing sequence compliance degree (fscd) of the as-ismodel with respect to the adopted reference model according to a secondequation:${{fscd}( {\sigma_{2},\sigma_{1},,} )} = \frac{{fsc}( {\sigma_{2},\sigma_{1},,} )}{{\sigma_{1}}_{map}}$wherein the second firing sequence σ₂ includes transitions, and whereinthe firing sequence compliance degree evaluates how many of thetransitions of the second firing sequence σ₂ are present in the firstfiring sequence σ₁ while preserving an activity order.
 7. Thecomputer-implemented method of claim 6, where calculating thesequence-based compliance measurement comprises: calculating acompliance degree (cd) of the as-is model with respect to the adoptedreference model according to a third equation:${{cd}( {M_{2},M_{1},,} )} = \frac{\sum\limits_{\sigma_{2} \in {S^{\prime}{(M_{2})}}}{\max\limits_{\sigma_{1} \in {S^{\prime}{(M_{1})}}}\{ {{fscd}( {\sigma_{2},\sigma_{1},,} )} \}}}{{S^{\prime}( M_{2} )}}$wherein the compliance degree indicates how many instances of a secondreference model M₂ are also present in a first reference model M₁. 8.The computer-implemented method of claim 5, where calculating thesequence-based compliance measurement comprises: calculating a firingsequence compliance maturity (fscm) of the as-is model with respect tothe adopted reference model according to a second equation:${{fscm}( {\sigma_{2},\sigma_{1},,} )} = \frac{{fsc}( {\sigma_{2},\sigma_{1},,} )}{{\sigma_{1}}_{ext}}$wherein the first firing sequence σ₁ includes transitions, and whereinthe firing sequence compliance maturity evaluates how many of thetransitions of the first firing sequence σ₁ are present in the secondfiring sequence σ₂ while preserving an activity order.
 9. Thecomputer-implemented method of claim 8, where calculating thesequence-based compliance measurement comprises: calculating acompliance maturity (cm) of the as-is model with respect to the adoptedreference model according to a third equation:${{cm}( {M_{2},M_{1},,} )} = \frac{\sum\limits_{\sigma_{1} \in {S^{\prime}{(M_{1})}}}{\max\limits_{\sigma_{2} \in {S^{\prime}{(M_{2})}}}\{ {{fscm}( {\sigma_{2},\sigma_{1},,} )} \}}}{{S^{\prime}( M_{1} )}}$wherein the compliance maturity indicates how many of the instances of afirst reference model M₁ are being followed by a second reference modelM₂.
 10. The computer-implemented method of claim 1, wherein the methodfurther comprises: adjusting a to-be model according to a granularityrelated to the adopted reference model.
 11. The computer-implementedmethod of claim 1, wherein the method further comprises: adjusting theas-is model according to an order partition related to the adoptedreference model.
 12. The computer-implemented method of claim 1, whereinthe method further comprises: adjusting the adopted reference modelaccording to an exclusion partition related to the adopted referencemodel.
 13. The computer-implemented method of claim 1, wherein themethod further comprises: adjusting the adopted reference modelaccording to a cycle related to the adopted reference model.
 14. Acomputer-readable medium embodying a computer program that controls acomputer system to measure process compliance, comprising: a storagemodule that controls the computer system to store an adopted referencemodel of a business process, and that controls the computer system tostore a plurality of process instances of the business process; ageneration module that controls the computer system to generate an as-ismodel from the plurality of process instances; a calculation module thatcontrols the computer system to calculate a sequence-based compliancemeasurement between the adopted reference model and the as-is model; andan output module that controls the computer system to output thesequence-based compliance measurement.
 15. A computer system formeasuring process compliance, comprising: a storage system that isconfigured to store a first model of a business process, and that isconfigured to store a second model of the business process; acalculation module that is configured to calculate a sequence-basedcompliance measurement between the first model and the second model; andan interface module that is configured to output the sequence-basedcompliance measurement.
 16. The computer system of claim 15, furthercomprising: a generation module that is configured to generate an as-ismodel from a plurality of process instances, wherein the as-is modelcorresponds to the second model.
 17. The computer system of claim 15,further comprising: a generation module that is configured to generatean as-is model from a plurality of process instances, wherein the as-ismodel corresponds to the second model; and a plurality of clientcomputers that record the plurality of process instances.
 18. Thecomputer system of claim 15, wherein the first model corresponds to anadopted reference model, and wherein the second model corresponds to anas-is model.
 19. The computer system of claim 15, wherein the firstmodel corresponds to an adopted reference model, and wherein the secondmodel corresponds to a to-be model.
 20. The computer system of claim 15,wherein the first model corresponds to a to-be model, and wherein thesecond model corresponds to an as-is model.